Arccos Calculator
Find the angle whose cosine is a given value, in degrees and radians. Results between 0° and 180°.
arccos(0.5) = 60°
arccos(0.5)
60°
In radians
1.0472 rad
Multiply degrees by π/180
Arccos is the inverse of cosine: it returns the angle whose cosine is the given value. The result always lies between 0° and 180°.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Arccos appears whenever a cosine ratio is measured before the angle is known. Structural engineers in India use it to find member angles from measured horizontal and diagonal lengths, and electricians use it for cable bending angles from run and drop measurements. A ladder-safety check measures the distance of a ladder's base from the wall and its length, then reads the lean angle with arccos — Indian factory safety officers commonly verify that ladders sit at about 75°. Astronomy students use arccos to find the angular separation of stars from coordinate measurements, and navigators compute course corrections from drift ratios. The tool's 0° to 180° range also suits problems involving obtuse angles, which arcsin cannot express. Physics students use the radians output directly in rotational mechanics and optics calculations.
How to Use This Calculator
- Step 1: Enter a cosine value between −1 and 1, such as 0.5.
- Step 2: Read the angle in degrees whose cosine equals that value.
- Step 3: Read the same angle in radians alongside it.
- Step 4: Check that the result lies between 0° and 180°, which is always true for arccos.
Worked Example
A physics student in Hyderabad measures the adjacent side of a right triangle as half the hypotenuse, a ratio of 0.5. arccos(0.5) returns 60°, and about 1.0472 radians, since cos(60°) = 0.5. Entering 1 gives 0°, meaning the sides coincide, while −1 gives 180°, a completely flipped direction. For the ratio 0.8660, close to √3/2, the calculator returns 30°. Used together with the cosine calculator, this tool closes the loop between a measured ratio and its angle for every board and entrance exam problem.
Tips and Common Mistakes
- •Tip 1: Like arcsin, the input must stay between −1 and 1 — the calculator explains when it is not.
- •Tip 2: Use arccos when the adjacent side and hypotenuse are known but the angle is not.
- •Tip 3: arccos(x) and arcsin(x) are complementary: their results add up to 90° for the same input.
- ✗Mistake 1: Entering the ratio the wrong way round — adjacent ÷ hypotenuse, not hypotenuse ÷ adjacent.
- ✗Mistake 2: Expecting negative angles from arccos — it spans 0° to 180°, unlike arcsin which spans −90° to 90°.
Frequently Asked Questions
What is arccos?
Arccos is the inverse of cosine: it answers 'which angle has this cosine value?' Since cos(60°) = 0.5, arccos(0.5) = 60°. It is also written as cos⁻¹.
Why must the input be between −1 and 1?
Cosine never returns values outside −1 to 1 for real angles, so arccos(2) has no real answer. The calculator returns a clear message for such inputs.
What is the range of arccos?
The result always lies between 0° and 180° (0 to π radians). arccos(1) = 0°, arccos(0) = 90°, and arccos(−1) = 180°.
How is arccos different from arcsin?
Arcsin answers for sine ratios, arccos for cosine ratios, and their outputs use different ranges: arcsin stays within ±90° while arccos spans 0° to 180°. They are related by arccos(x) = 90° − arcsin(x).
When would I use arccos in real life?
When an angle is best measured through its adjacent side: finding the lean angle of a ladder from the distance of its base to the wall, or the phase angle of AC current from a power factor reading.
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